Use the image to answer the question.

Question

An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 10 right parenthesis and left parenthesis 1 comma negative 7 right parenthesis.

Is this the correct graph of 3x−y=10
?

(1 point)
Responses

Yes, it is the correct graph because the slope is −3
and the y-intercept is (0, −10)

No, it is not the correct graph because the slope is −3
and the y-intercept is (0, −10)

No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10

Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10)

Answer 1

To determine if the graph represents the equation $3x-y=10$, we need to rewrite the equation in slope-intercept form, $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

Starting with the equation: $$3x-y=10$$ Rearranging it to solve for $y$: $$-y=-3x+10$$ $$y=3x-10$$

From this, we can see that the slope ($m$) is $3$ and the y-intercept ($b$) is $(0,-10)$.

Now, looking at the information provided regarding the graph:

• The statement mentions that the line has a slope of $-3$, but we determined it to be $3$.
• The y-intercept is indeed at $(0,-10)$.

Since the graph has the correct y-intercept but the slope is incorrect (it should be $3$ instead of $-3$), the correct response is:

No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10).